phase_space_to_astrometry#

pygaia.astrometry.vectorastrometry.phase_space_to_astrometry(x, y, z, vx, vy, vz)#

From the given phase space coordinates calculate the astrometric observables, including the radial velocity, which here is seen as the sixth astrometric parameter. The phase space coordinates are assumed to represent barycentric (i.e. centred on the Sun) positions and velocities.

Parameters:

  • x (float or float array) – The x component of the barycentric position vector (in pc or kpc).

  • y (float or float array) – The y component of the barycentric position vector (in pc or kpc).

  • z (float or float array) – The z component of the barycentric position vector (in pc or kpc).

  • vx (float or float array) – The x component of the barycentric velocity vector (in km/s).

  • vy (float or float array) – The y component of the barycentric velocity vector (in km/s).

  • vz (float or float array) – The z component of the barycentric velocity vector (in km/s).

Returns:

  • phi (float or float array) – The longitude-like angle of the position of the source (radians).

  • theta (float or float array) – The latitude-like angle of the position of the source (radians).

  • parallax (float or float array) – The parallax of the source (in mas or muas, see notes)

  • muphistar (float or float array) – The proper motion in the longitude-like angle, multiplied by cos(theta) (mas/yr or muas/yr, see notes)

  • mutheta (float or float array) – The proper motion in the latitude-like angle (mas/yr or muas/yr, see notes)

  • vrad (float or float array) – The radial velocity (km/s)

Notes

This function has no mechanism to deal with units. The velocity units are always assumed to be km/s, and the code is set up such that for positions in pc, the return units for the astrometry are radians, milliarcsec, milliarcsec/year and km/s. For positions in kpc the return units are: radians, microarcsec, microarcsec/year, and km/s.

The doppler factor \(k=1/(1-v_\mathrm{rad}/c)\) is not used in the calculations. This is not a problem for sources moving at typical velocities of Galactic stars.